T / MTBF e-T / MTBF T / MTBF e-T / MTBF T / MTBF e-T / MTBF 0.10 .9048 2.60 .074
ID: 438781 • Letter: T
Question
T / MTBF e-T / MTBF T / MTBF e-T / MTBF T / MTBF e-T / MTBF 0.10 .9048 2.60 .0743 5.10 .0061 0.20 .8187 2.70 .0672 5.20 .0055 0.30 .7408 2.80 .0608 5.30 .0050 0.40 .6703 2.90 .0550 5.40 .0045 0.50 .6065 3.00 .0498 5.50 .0041 0.60 .5488 3.10 .0450 5.60 .0037 0.70 .4966 3.20 .0408 5.70 .0033 0.80 .4493 3.30 .0369 5.80 .0030 0.90 .4066 3.40 .0334 5.90 .0027 1.00 .3679 3.50 .0302 6.00 .0025 1.10 .3329 3.60 .0273 6.10 .0022 1.20 .3012 3.70 .0247 6.20 .0020 1.30 .2725 3.80 .0224 6.30 .0018 1.40 .2466 3.90 .0202 6.40 .0017 1.50 .2231 4.00 .0183 6.50 .0015 1.60 .2019 4.10 .0166 6.60 .0014 1.70 .1827 4.20 .0150 6.70 .0012 1.80 .1653 4.30 .0136 6.80 .0011 1.90 .1496 4.40 .0123 6.90 .0010 2.00 .1353 4.50 .0111 7.00 .0009 2.10 .1255 4.60 .0101 2.20 .1108 4.70 .0091 2.30 .1003 4.80 .0082 2.40 .0907 4.90 .0074 2.50 .0821 5.00 .0067 -------------------------------------------------------------------------------- a. If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fail during the service period? 1Explanation / Answer
Since the mean of the exponential is 30, the pdf is f(x)=(1/30)e^(-x/30) Integrating (0 to x), we find that the cdf is F(x) = 1-e^(-x/30) Remember the cdf is the probability the unit will fail before x. I'm not going to do your homework for you, but I'll do (1) from each set. A1) The probability that the unit lasts at least 39 months is 1-(the probability the unit will fail before 39 months) 1-F(39) e^(-39/30) [I don't have a calculator, so I'll leave that to you.] B1) This is the exact definition of the cdf, so just calculate F(33): F(33) 1-e^(-33/30) C1) We've been calculating the probability/percentage this whole time. It's what the cdf equals. So, to find the length before 50 percent fail, we want to find x such that F(x)=0.5 F(x) = 0.5 1-e^(-x/30) = 0.5 e^(-x/30) = 0.5 [subtract 1 from both sides and multiply by -1] -x/30 = ln(0.5) x = -30*ln(0.5) [after you get the answer, remember it's in months]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.